69). If area of a square is 64 sq cm, then find the area of the circle formed by the same perimeter.

A). \( \Large 25 cm^{2} \)

B). \( \Large 1.25 cm^{2} \)

C). \( \Large 12 cm^{2} \)

D). None of the above

View Answer

Correct Answer: \( \Large 12 cm^{2} \)

ABCD be the rectangle inscribed in the circle of diameter 5 cm. Diameter = Diagonal of rectangle

Now, let x and y be the lengths and breadths of rectangle, respectively.

Now, in \( \Large \triangle ABD \)

\( \Large AB^{2}+AD^{2}=(5)^{2} \)

=> \( \Large x^{2}+y^{2} \)=25

Since, they form Pythagoras theorem.

So,x=4 and y=3

Area of rectangle = \( \Large 3\times 4=12 cm^{2} \)

70). The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 72 cm and the length of the rectangle is 12 cm. what is the difference between the breadth of the rectangle and the Side of the square?